Why Do We Need Statistics?
Types of Data Analysis
Quantitative Methods: Testing theories using numbers
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Please rate the followng question on a scale from 1-7, 1 meaning not at all and 7 meaning extremely
- How happy are you?
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Please rate the following statement on a 1-7 scale, 1 meaning stronly disagree and 7 meaning strongly agree
- I love Animal Corssing
Qualitative Methods: Testing theories using language
- Magazine articles/Interviews
- Conversations
- Newspapers
- Media broadcasts
The Research Process
Figure 1.2 DSUR
Initial Observation
Find something that needs explaining
- Observe the real world
- Read other research
Test the concept: collect data
- Collect data to see whether your hunch is correct
- To do this you need to define variables
Generating and Testing Theories
Figure 1.2 DSUR
Theory: A hypothesized general principle or set of principles that explains known findings about a topic and from which new hypotheses can be generated.
- Social Learning Theory: People learn by observing others
Hypothesis: A prediction from a theory.
- The YouTube influencer is a good case in point. If you like a particular influencer you may well want to model your behavior after theirs. If they enjoys a certain brand of shampoo, then you may well imitate them by purchasing that brand.
- The number of people turning up for a Big Brother audition that have narcissistic personality disorder will be higher than the general level (1%) in the population.
Table 1.1 DSUR
Falsification: The act of disproving a theory or hypothesis.
Data Collection: What to Measure?
Figure 1.2 DSUR
Hypothesis: Coca-Cola kills sperm
Independent Variable: The proposed cause
- Statistics: A predictor variable
- A manipulated variable (in experiments)
- Coca-Cola in the hypothesis above
Dependent Variable: The proposed effect
- Statitics: An outcome variable
- Measured not manipulated (in experiments)
- Sperm in the hypothesis above
Levels of Measurement
Categorical: entities are divided into distinct categories
- Binary variable: There are only two categories
- e.g. dead or alive.
- Nominal variable: There are more than two categories
- e.g. whether someone is an omnivore, vegetarian, vegan, or fruitarian.
- Ordinal variable: The same as a nominal variable but the categories have a logical order
- e.g. whether people got a fail, a pass, a merit or a distinction in their exam.
Continuous: entities get a distinct score
- Interval variable: Equal intervals on the variable represent equal differences in the property being measured
- e.g. the difference between 6 and 8 is equivalent to the difference between 13 and 15.
- Ratio variable: The same as an interval variable, but the ratios of scores on the scale must also make sense
- e.g. a score of 16 on an anxiety scale means that the person is, in reality, twice as anxious as someone scoring 8.
Measurement error
Measurement error: The discrepancy between the actual value we’re trying to measure, and the number we use to represent that value.
Example:
You (in reality) weigh 80 kg.
You stand on your bathroom scales and they say 83 kg.
The measurement error is 3 kg.
Validity
Validity: Whether an instrument measures what it set out to measure.
Content validity: Evidence that the content of a test corresponds to the content of the construct it was designed to cover
Ecological validity: Evidence that the results of a study, experiment or test can be applied, and allow inferences, to real-world conditions
Reliability
Reliability: The ability of the measure to produce the same results under the same conditions.
Test–Retest Reliability: The ability of a measure to produce consistent results when the same entities are tested at two different points in time.
How to Measure
Correlational research: Observing what naturally goes on in the world without directly interfering with it.
Cross-sectional research: This term implies that data come from people at different age points, with different people representing each age point.
Experimental research: One or more variable is systematically manipulated to see their effect (alone or in combination) on an outcome variable. Statements can be made about cause and effect
Experimental Research Methods
Cause and Effect (Hume, 1748) require 3 components of research design:
- Cause and effect must occur close together in time (contiguity)
- The cause must occur before an effect does (temporal precedence)
- Address confounding varables
Confounding variables: A variable (that we may or may not have measured) other than the predictor variables that potentially affects an outcome variable
- e.g. the relationship between breast implants and suicide is confounded by self-esteem. Ruling out confounds (Mill, 1865)
Control conditions: The cause is absent. An effect should be present when the cause is present and that when the cause is absent the effect should be absent also.
- e.g. Coffee increases energy. Coffee is the cause of increased energy. If you do not drink your morning coffee (cause is absent) your energy should not increase
Methods of Data Collection
Between-group/between-subject/independent: Different entities (participants) in experimental conditions
- e.g. Bring 100 people into the lab individually. You give 50 coffee to drink and 50 water to drink. You then measure their heart rate
Repeated-measures (within-subject): The same entities (participants) take part in all experimental conditions.
- e.g. Bring 50 people into the lab individually. You them all coffee to drink and measure their heart rate. Then, you give the SAME 50 people water to drink and then measure their heart rate
- Economical
- Practice effects
- Fatigue
Types of Variation
Systematic Variation: Differences in performance created by a specific experimental manipulation
Unsystematic Variation: Differences in performance created by unknown factors
- Age, gender, IQ, time of day, measurement error, etc.
Randomization: Minimizes unsystematic variation
Analyzing Data
Figure 1.2 DSUR
Histograms
Histograms: Visualize Frequency Distributions. A graph plotting values of observations on the horizontal axis, with a bar showing how many times each value occurred in the data set.
The ‘Normal’ Distribution: Bell-shaped & Symmetrical around the center
Figure 1.3 DSUR
Properties of Frequency Distributions
Skew: The symmetry of the distribution
Positive skew = scores bunched at low values with the tail pointing to high values
Negative skew = scores bunched at high values with the tail pointing to low values
Figure 1.4 DSUR
Kurtosis: The ‘heaviness’ of the tails
Leptokurtic = heavy tails
Platykurtic = light tails
Figure 1.5 DSUR
Central Tendency
Central tendency: The Mode
Mode: The most frequent score
Bimodal: Having two modes
Figure 1.6 DSUR
Multimodal: Having several modes
Central Tendency: The Median
Median: The middle score when scores are ordered
Example: Number of friends of 11 Facebook users
Central Tendency: The Mean
Mean: The sum of scores divided by the number of scores
Example: Number of friends of 11 Facebook users
The Dispersion
The Dispersion: Range
The Range: The smallest score subtracted from the largest
Example
Number of friends of 11 Facebook users from lowest to highest
22, 40, 53, 57, 93, 98, 103, 108, 116, 121, 252
Range = 252 – 22 = 230
Very biased by outliers
The Dispersion: The Interquartile range
Quartiles: The three values that split the sorted data into four equal parts
Second quartile = median. Lower quartile = median of lower half of the data. Upper quartile = median of upper half of the data.
Figure 1.7 DSUR
Going beyond the data: z-scores
z-scores: Standardizing a score with respect to the other scores in the group. Expresses a score in terms of how many standard deviations it is away from the mean. The distribution of z-scores has a mean of 0 and SD = 1.
Properties of z-scores
- 1.96 cuts off the top 2.5% of the distribution
- −1.96 cuts off the bottom 2.5% of the distribution
- As such, 95% of z-scores lie between −1.96 and 1.96
- 99% of z-scores lie between −2.58 and 2.58
- 99.9% of them lie between −3.29 and 3.29
Types of Hypotheses
Null hypothesis, H0: There is no effect
E.g. Big Brother contestants and members of the public will not differ in their scores on personality disorder questionnaires
The alternative hypothesis, H1: Aka the experimental hypothesis
E.g. Big Brother contestants will score higher on personality disorder questionnaires than members of the public